A Smooth Trajectory Generation Algorithm for Addressing Higher-Order Dynamic Constraints in Nanopositioning Systems

Bharathi, Akilan; Dong, Jingyan

doi:10.1016/j.promfg.2015.09.006

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…In [18], [19], [20], the authors approximated the optimal profiles by a piece-wise polynomial in the (s,ṡ) plane. The polynomials are controlled via a finite set of knot points.…”

Section: A Related Workmentioning

confidence: 99%

On the structure of the time-optimal path parameterization problem with third-order constraints

Phạm

Pham

2017

2017 IEEE International Conference on Robotics and Automation (ICRA)

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Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and wellstudied problem in robotics. In comparison, TOPP subject to third-order constraints (e.g. jerk, torque rate, etc.) has received far less attention and remains largely open. In this paper, we investigate the structure of the TOPP problem with third-order constraints. In particular, we identify two major difficulties: (i) how to smoothly connect optimal profiles, and (ii) how to address singularities, which stop profile integration prematurely. We propose a new algorithm, TOPP3, which addresses these two difficulties and thereby constitutes an important milestone towards an efficient computational solution to TOPP with thirdorder constraints.

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“…In [18], [19], [20], the authors approximated the optimal profiles by a piece-wise polynomial in the (s,ṡ) plane. The polynomials are controlled via a finite set of knot points.…”

Section: A Related Workmentioning

confidence: 99%

On the structure of the time-optimal path parameterization problem with third-order constraints

Phạm

Pham

2017

2017 IEEE International Conference on Robotics and Automation (ICRA)

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“…An algorithm for computing such a function with piecewise constant jerk ("seven segment profile") was presented by the author in [4], where restrictions on velocity, acceleration, and jerk and boundary conditions regarding velocity and acceleration can be prescribed. If there are stronger requirements on vibration reduction (e.g., for restricting position errors), higher-order continuity of the motion function has proven to be effective in experimental settings [5][6][7][8][9][10][11][12]. In this contribution, we present an algorithm for computing a jerk-continuous motion function (as opposed to the piecewise-constant, discontinuous jerk function designed in [4]) in one dimension, such that symmetric restrictions regarding velocity, acceleration, jerk, and snap (the derivative of the jerk, abbreviated as sn in the sequel) are fulfilled and boundary 2 of 39 conditions for position and velocity can be arbitrarily prescribed.…”

Section: Introductionmentioning

confidence: 99%

On Fast Jerk-Continuous Motion Functions with Higher-Order Kinematic Restrictions for Online Trajectory Generation

Alpers

2022

Robotics

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In robotics and automated manufacturing, motion functions for parts of machines need to be designed. Many proposals for the shape of such functions can be found in the literature. Very often, time efficiency is a major criterion for evaluating the suitability for a given task. If there are higher precision requirements, the reduction in vibration also plays a major role. In this case, motion functions should have a continuous jerk function but still be as fast as possible within the limits of kinematic restrictions. The currently available motion designs all include assumptions that facilitate the computation but are unnecessary and lead to slower functions. In this contribution, we drop these assumptions and provide an algorithm for computing a jerk-continuous fifteen segment profile with arbitrary initial and final velocities where given kinematic restrictions are met. We proceed by going systematically through the design space using the concept of a varying intermediate velocity and identify critical velocities and jerks where one has to switch models. The systematic approach guarantees that all possible situations are covered. We implemented and validated the model using a huge number of random configurations in Matlab, and we show that the algorithm is fast enough for online trajectory generation. Examples illustrate the improvement in time efficiency compared to existing approaches for a wide range of configurations where the maximum velocity is not held over a period of time. We conclude that faster motion functions are possible at the price of an increase in complexity, yet which is still manageable.

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Optimal trajectory tracking solution: Fractional order viewpoint

Razminia

Asadizadehshiraz

Shaker

2019

Journal of the Franklin Institute

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A Smooth Trajectory Generation Algorithm for Addressing Higher-Order Dynamic Constraints in Nanopositioning Systems

Cited by 4 publications

References 8 publications

On the structure of the time-optimal path parameterization problem with third-order constraints

On the structure of the time-optimal path parameterization problem with third-order constraints

On Fast Jerk-Continuous Motion Functions with Higher-Order Kinematic Restrictions for Online Trajectory Generation

Optimal trajectory tracking solution: Fractional order viewpoint

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